E8 Root-Gated Phi-Harmonic Stabilization of Polygonal Billiard Orbits — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
By projecting the 240 root vectors of E8 onto its 30 distinguished Coxeter planes, we obtain a set of phi‑weighted geometric thresholds that can be used to gate the reflection law in outer billiards on regular polygons. When these thresholds modulate the billiard map, orbits that are normally unbounded become stable precisely when the polygon's number of vertices shares a divisor with the multiplicity pattern of the projected roots. This stabilization exhibits a phi‑harmonic resonance tied to the 132 Hz base frequency, predicting quantized recurrence times that bridge classical billiard dynamics and quantum coherent cycles in E8‑scaled cavities.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026rootgated,
title = {{E8 Root-Gated Phi-Harmonic Stabilization of Polygonal Billiard Orbits — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23446660},
url = {https://zenodo.org/records/23446660},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Root-Gated Phi-Harmonic Stabilization of Polygonal Billiard Orbits — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23446660
UR - https://zenodo.org/records/23446660
AB - By projecting the 240 root vectors of E8 onto its 30 distinguished Coxeter planes, we obtain a set of phi‑weighted geometric thresholds that can be used to gate the reflection law in outer billiards on regular polygons. When these thresholds modulate the billiard map, orbits that are normally unbounded become stable precisely when the polygon's number of vertices shares a divisor with the multiplicity pattern of the projected roots. This stabilization exhibits a phi‑harmonic resonance tied to the 132 Hz base frequency, predicting quantized recurrence times that bridge classical billiard dynamics and quantum coherent cycles in E8‑scaled cavities. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -